The average of 11 numbers is 28. If the average of first 5 numbers is 23 and the average of next 5 numbers is 25, then find the 11th number

Options

A. 68
B. 58
C. 73
D. 63

Answer

To find the 11th number given the average of 11 numbers, we can follow these steps:

### Step 1: Calculate the total sum of the 11 numbers
The average of 11 numbers is given as 28. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of terms}}{\text{Number of terms}} \]
So, we can rearrange this to find the sum:
\[ \text{Sum of 11 numbers} = \text{Average} \times \text{Number of terms} = 28 \times 11 = 308 \]

### Step 2: Calculate the sum of the first 5 numbers
The average of the first 5 numbers is given as 23. Using the same formula:
\[ \text{Sum of first 5 numbers} = \text{Average} \times \text{Number of terms} = 23 \times 5 = 115 \]

### Step 3: Calculate the sum of the next 5 numbers
The average of the next 5 numbers is given as 25. Again, using the average formula:
\[ \text{Sum of next 5 numbers} = \text{Average} \times \text{Number of terms} = 25 \times 5 = 125 \]

### Step 4: Calculate the sum of the first 10 numbers
Now, we can find the total sum of the first 10 numbers by adding the sums of the first 5 and the next 5:
\[ \text{Sum of first 10 numbers} = \text{Sum of first 5 numbers} + \text{Sum of next 5 numbers} = 115 + 125 = 240 \]

### Step 5: Find the 11th number
Now, we can find the 11th number by subtracting the sum of the first 10 numbers from the total sum of the 11 numbers:
\[ \text{11th number} = \text{Sum of 11 numbers} - \text{Sum of first 10 numbers} = 308 - 240 = 68 \]

Thus, the 11th number is **68**.

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